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On the Intuitionistic Fuzzy Topological Structures of Rough Intuitionistic Fuzzy Sets

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Book cover Transactions on Rough Sets XVIII

Part of the book series: Lecture Notes in Computer Science ((TRS,volume 8449))

Abstract

A rough intuitionistic fuzzy set is the result of approximation of an intuitionistic fuzzy set with respect to a crisp approximation space. In this paper, we investigate topological structures of rough intuitionistic fuzzy sets. We first show that a reflexive crisp rough approximation space can induce an intuitionistic fuzzy Alexandrov space. It is proved that the lower and upper rough intuitionistic fuzzy approximation operators are, respectively, an intuitionistic fuzzy interior operator and an intuitionistic fuzzy closure operator if and only if the binary relation in the crisp approximation space is reflexive and transitive. We then verify that a similarity crisp approximation space can produce an intuitionistic fuzzy clopen topological space. We further examine sufficient and necessary conditions that an intuitionistic fuzzy interior (closure, respectively) operator derived from an intuitionistic fuzzy topological space can associate with a reflexive and transitive crisp relation such that the induced lower (upper, respectively) rough intuitionistic fuzzy approximation operator is exactly the intuitionistic fuzzy interior (closure, respectively) operator.

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Acknowledgments

This work was supported by grants from the National Natural Science Foundation of China (Nos. 61272021, 61075120, 11071284, 61202206, and 61173181), the Zhejiang Provincial Natural Science Foundation of China (No. LZ12F03002), and Chongqing Key Laboratory of Computational Intelligence (No. CQ-LCI-2013-01).

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Authors and Affiliations

  1. School of Mathematics, Physics and Information Science, Zhejiang Ocean University, Zhoushan, 316022, Zhejiang, People’s Republic of China

    You-Hong Xu & Wei-Zhi Wu

  2. Chongqing Key Laboratory of Computational Intelligence, Chongqing University of Posts and Telecommunications, Chongqing, 400065, People’s Republic of China

    You-Hong Xu, Wei-Zhi Wu & Guoyin Wang

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  1. You-Hong Xu
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  2. Wei-Zhi Wu
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  3. Guoyin Wang
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Correspondence to Wei-Zhi Wu .

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Editors and Affiliations

  1. ECE Department Computational Intelligence Laboratory, University of Manitoba, Winnipeg, MB, Canada

    James F. Peters

  2. University of Warsaw, Warsaw, Poland

    Andrzej Skowron  & Hung Son Nguyen  & 

  3. Southwest Jiaotong University, Sichuan, China

    Tianrui Li  & Yan Yang  & 

  4. University of Regina, Regina, SK, Canada

    JingTao Yao

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Xu, YH., Wu, WZ., Wang, G. (2014). On the Intuitionistic Fuzzy Topological Structures of Rough Intuitionistic Fuzzy Sets. In: Peters, J.F., Skowron, A., Li, T., Yang, Y., Yao, J., Nguyen, H.S. (eds) Transactions on Rough Sets XVIII. Lecture Notes in Computer Science(), vol 8449. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-44680-5_1

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  • DOI: https://doi.org/10.1007/978-3-662-44680-5_1

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  • Print ISBN: 978-3-662-44679-9

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